Randomized Model Order Reduction

TL;DR

This paper introduces a randomized SVD approach to efficiently compute basis functions for model order reduction, significantly reducing computational costs in techniques like POD and DMD while maintaining accuracy.

Contribution

It presents a novel application of randomized matrix decompositions to improve the efficiency of basis computation in model order reduction methods.

Findings

Randomized SVD reduces computational cost significantly.

The method maintains high accuracy in basis function computation.

Numerical tests confirm effectiveness for POD and DMD.

Abstract

Singular value decomposition (SVD) has a crucial role in model order reduction. It is often utilized in the offline stage to compute basis functions that project the high-dimensional nonlinear problem into a low-dimensionsl model which is, then, evaluated cheaply. It constitutes a building block for many techniques such as e.g. Proper Orthogonal Decomposition and Dynamic Mode Decomposition. The aim of this work is to provide efficient computation of the basis functions via randomized matrix decompositions. This is possible due to the randomized Singular Value Decomposition (rSVD) which is a fast and accurate alternative of the SVD. Although this is considered as offline stage, this computation may be extremely expensive and therefore the use of compressed techniques drastically reduce its cost. Numerical examples show the effectiveness of the method for both Proper Orthogonal Decomposition (POD) and Dynamic Mode Decomposition (DMD).